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The design of novel algorithms for solving inverse problems in signal processing is an incredibly difficult, heuristic-driven, and time-consuming task. In this short paper, we the idea of automated algorithm discovery in the signal…
In this paper we consider the problem of exact recovery of a fixed sparse vector with the measurement matrices sequentially arriving along with corresponding measurements. We propose an extension of the iterative hard thresholding (IHT)…
In this paper, we present modifications of the iterative hard thresholding (IHT) method for recovery of jointly row-sparse and low-rank matrices. In particular a Riemannian version of IHT is considered which significantly reduces…
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
Modern scientific instruments produce vast amounts of data, which can overwhelm the processing ability of computer systems. Lossy compression of data is an intriguing solution, but comes with its own drawbacks, such as potential signal…
This paper investigates the sparse phase retrieval problem, which aims to recover a sparse signal from a system of quadratic measurements. In this work, we propose a novel non-convex algorithm, termed Gradient Hard Thresholding Pursuit…
In this paper, we generalize Huber's criterion to multichannel sparse recovery problem of complex-valued measurements where the objective is to find good recovery of jointly sparse unknown signal vectors from the given multiple measurement…
Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, the existing…
Compressed sensing has been a very successful high-dimensional signal acquisition and recovery technique that relies on linear operations. However, the actual measurements of signals have to be quantized before storing or processing.…
A novel algorithm for the recovery of low-rank matrices acquired via compressive linear measurements is proposed and analyzed. The algorithm, a variation on the iterative hard thresholding algorithm for low-rank recovery, is designed to…
A spectrally sparse signal of order $r$ is a mixture of $r$ damped or undamped complex sinusoids. This paper investigates the problem of reconstructing spectrally sparse signals from a random subset of $n$ regular time domain samples, which…
The problem of the distributed recovery of jointly sparse signals has attracted much attention recently. Let us assume that the nodes of a network observe different sparse signals with common support; starting from linear, compressed…
The idea of unfolding iterative algorithms as deep neural networks has been widely applied in solving sparse coding problems, providing both solid theoretical analysis in convergence rate and superior empirical performance. However, for…
Adaptive thresholding methods have proved to yield high SNRs and fast convergence in finding the solution to the Compressed Sensing (CS) problems. Recently, it was observed that the robustness of a class of iterative sparse recovery…
Finding the sparset solution of an underdetermined system of linear equations $y=Ax$ has attracted considerable attention in recent years. Among a large number of algorithms, iterative thresholding algorithms are recognized as one of the…
We provide another framework of iterative algorithms based on thresholding, feedback and null space tuning for sparse signal recovery arising in sparse representations and compressed sensing. Several thresholding algorithms with various…
This paper introduces recovery thresholding hyperinterpolations, a novel class of methods for sparse signal reconstruction in the presence of noise. We develop a framework that integrates thresholding operators--including hard thresholding,…
Commonly employed reconstruction algorithms in compressed sensing (CS) use the $L_2$ norm as the metric for the residual error. However, it is well-known that least squares (LS) based estimators are highly sensitive to outliers present in…
Sparse signal recovery is one of the most fundamental problems in various applications, including medical imaging and remote sensing. Many greedy algorithms based on the family of hard thresholding operators have been developed to solve the…
The use of M-estimators in generalized linear regression models in high dimensional settings requires risk minimization with hard $L_0$ constraints. Of the known methods, the class of projected gradient descent (also known as iterative hard…